CentOS is the compiled bits of "a prominent North American enterprise linux vendor." If you get your secret decoder ring out, that spells "RedHat Enterprise Linux." As such, CentOS by default only includes the more stable applications and repositories. There are also many service organizations that will, for a fee, support its use as a server.
Fedora, on the other hand, is a direct RedHat product (or rather, a "RedHat sponsored community project") and is considered something of a testing grounds for updates, patches and packages. It has more "cutting edge" and somewhat experimental packages that could introduce instability and security flaws. That's fine for everyday desktop use in an informal environment (I've been using Fedora for about 7 months now with no serious issues), but it is completely unacceptable in a business environment where stability and predictability are paramount.
If your use of the word "performance" means pure application speed, there is no advantage when comparing the two. I suppose someone could make the argument that newer versions of applications that have speed improvements are available in the more cutting edge repositories, but that's something of an edge case, IMO. Of course, you can always add those more cutting edge repositories if you choose. However, before you do, read the next paragraph first.
If "performance" means a holistic view towards stability and security (which it typically doesn't, but I'll include that possibility to be thorough) then CentOS will have the clear advantage. Of course, you can stomp all over that advantage if you include a ton of bleeding edge repositories and start installing the latest and greatest alpha builds of everything in sight.